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If vm is not equal to 0, is vm > 0?

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If vm is not equal to 0, is vm > 0?

by gmattesttaker2 » Sun Mar 30, 2014 10:33 pm
Hello,

Can you please help with solving Statement2 ?

If vm is not equal to 0, is vm > 0?

1) (v^2)m = v(m^2)
2) |m|v = |v|m

OA: D


1) vvm = vmm
=> v = m
=> vm > 0 . Suff.


2) |m|v = |v|m
=> |m|/|v| = m/v

However, I was not sure how to proceed from here. Can you please assist?

Thanks a lot,
Sri
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Source: — Data Sufficiency |

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by Brent@GMATPrepNow » Sun Mar 30, 2014 10:40 pm
gmattesttaker2 wrote:Hello,

Can you please help with solving Statement2 ?

If vm is not equal to 0, is vm > 0?

1) (v^2)m = v(m^2)
2) |m|v = |v|m

OA: D


1) vvm = vmm
=> v = m
=> vm > 0 . Suff.


2) |m|v = |v|m
=> |m|/|v| = m/v

However, I was not sure how to proceed from here. Can you please assist?

Thanks a lot,
Sri
You're almost there, Sri.
If |m|/|v| = m/v then we know that m/v is positive.
If m/v is positive, then vm is also positive.

Cheers,
Brent
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by Brent@GMATPrepNow » Sun Mar 30, 2014 10:52 pm
gmattesttaker2 wrote:Hello,

Can you please help with solving Statement2 ?

If vm is not equal to 0, is vm > 0?

1) v²m = vm²
2) |m|v = |v|m
The important rule at play here is that, if the QUOTIENT of two numbers is positive, then the PRODUCT of those same two numbers must also be positive.
For example, 6/3 is positive, and (6)(3) is also positive
Likewise, (-8)/(-4) is positive, and (-8)(-4) is also positive

Target question: Is vm positive?

Given: vm ≠ 0
In other words, v ≠ 0 and m ≠ 0

Statement 1: v²m = vm²
Take v²m = vm²
Divide both sides by v² to get: m = (vm²)/v²
Divide both sides by v to get: m/v = m²/v²
IMPORTANT: If v ≠ 0 and m ≠ 0, then v² is positive and m² is positive.
So, we get: m/v = (positive)/(positive)
In other words, m/v = some positive value
By the red rule above, we can conclude that mv is positive
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: |m|v = |v|m
Take |m|v = |v|m
Divide both sides by m to get: (|m|v)/m = |v|
Divide both sides by |m| to get: v/m = |v|/|m|
IMPORTANT: If v ≠ 0 and m ≠ 0, then |v| is positive and |m| is positive.
So, we get: v/m = (positive)/(positive)
In other words, v/m = some positive value
By the red rule above, we can conclude that mv is positive
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer = D

Cheers,
Brent
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by gmattesttaker2 » Mon Mar 31, 2014 8:49 pm
Brent@GMATPrepNow wrote:
gmattesttaker2 wrote:Hello,

Can you please help with solving Statement2 ?

If vm is not equal to 0, is vm > 0?

1) v²m = vm²
2) |m|v = |v|m
The important rule at play here is that, if the QUOTIENT of two numbers is positive, then the PRODUCT of those same two numbers must also be positive.
For example, 6/3 is positive, and (6)(3) is also positive
Likewise, (-8)/(-4) is positive, and (-8)(-4) is also positive

Target question: Is vm positive?

Given: vm ≠ 0
In other words, v ≠ 0 and m ≠ 0

Statement 1: v²m = vm²
Take v²m = vm²
Divide both sides by v² to get: m = (vm²)/v²
Divide both sides by v to get: m/v = m²/v²
IMPORTANT: If v ≠ 0 and m ≠ 0, then v² is positive and m² is positive.
So, we get: m/v = (positive)/(positive)
In other words, m/v = some positive value
By the red rule above, we can conclude that mv is positive
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: |m|v = |v|m
Take |m|v = |v|m
Divide both sides by m to get: (|m|v)/m = |v|
Divide both sides by |m| to get: v/m = |v|/|m|
IMPORTANT: If v ≠ 0 and m ≠ 0, then |v| is positive and |m| is positive.
So, we get: v/m = (positive)/(positive)
In other words, v/m = some positive value
By the red rule above, we can conclude that mv is positive
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer = D

Cheers,
Brent
Hello Brent,

Thanks for your awesome explanation and for explaining everything so clearly. Many thanks again.

Best Regards,
Sri
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